Bending Moment in Membrane Theory

Guy Bouchitté
Département de Mathématiques
Université de Toulon et du Var-BP 132
83957 La Garde Cedex, France
bouchitte@univ-tln.fr

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213, USA
fonseca@andrew.cmu.edu

M. Luisa Mascarenhas
C.M.A.F., Universidade de Lisboa
Av. Prof. Gama Pinto 2
16499-003 Lisboa Codex, Portugal
mascar@ptmat.fc.ul.pt

Abstract: A model of nonlinear membrane is proposed where the external loading induces a density of bending moments. The mathematical justification of this model is obtained through a 3D-2D dimension reduction via a $\Gamma$-convergence analysis taking into account the Cosserat vector field.


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